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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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A note on solid partitions
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by Donald E. Knuth PDF
Math. Comp. 24 (1970), 955-961 Request permission

Abstract:

The problem of enumerating partitions which satisfy a given partial order relation is reduced to the problem of enumerating permutations satisfying that relation. This theorem is applied to the enumeration of solid partitions; existing tables of solid partitions are extended.
References
  • A. O. L. Atkin, P. Bratley, I. G. Macdonald, and J. K. S. McKay, Some computations for $m$-dimensional partitions, Proc. Cambridge Philos. Soc. 63 (1967), 1097–1100. MR 217029, DOI 10.1017/s0305004100042171
  • Edward A. Bender and Donald E. Knuth, Enumeration of plane partitions, J. Combinatorial Theory Ser. A 13 (1972), 40–54. MR 299574, DOI 10.1016/0097-3165(72)90007-6
  • Donald E. Knuth, The art of computer programming, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975. Volume 1: Fundamental algorithms. MR 0378456
  • Major P. A. MacMahon, "Memoir on the theory of the partitions of numbers. V: Partitions in two-dimensional space," Philos. Trans. Roy. Soc London Ser. A, v. 211, 1912, pp. 75–110. Major P. A. MacMahon, "Memoir on the theory of the partitions of numbers. VI: Partitions in two-dimensional space, to which is added an adumbration of the theory of the partitions in three-dimensional space," Philos. Trans. Roy. Soc. London Ser. A, v. 211, 1912, pp. 345–373.
  • Percy A. MacMahon, Combinatory analysis, Chelsea Publishing Co., New York, 1960. Two volumes (bound as one). MR 0141605
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 955-961
  • MSC: Primary 05.10; Secondary 10.00
  • DOI: https://doi.org/10.1090/S0025-5718-1970-0277401-7
  • MathSciNet review: 0277401